Leonid Knizhnerman — list of papers and patents

Список статей

  1. L. A. Knizhnerman
    Krylov and rational Krylov methods of numerical solution of some problems of computational geophysics (in Russian)
    Journal of Geophysical Technologies, 2024, No 1, p. 29-46.
  2. M.A. Botchev, L. Knizhnerman, M. Schweitzer
    Krylov subspace residual and restarting for certain second order differential equations
    SISC, SPECIAL SECTION Copper Mountain 2022, 2024, v. 46, issue 2,  p. S223-S253.
  3. Leonid Knizhnerman; collarorators: Mikhail A. Botchev and Marcel Schweitzer
    The Arnoldi and Lanczos methods: residual estimates for some differential equations
    A talk at MMMA-2023
  4. Nikolay R. Ikonomov, Leonid A. Knizhnerman, Sergey P. Suetin
    Rational Hermite-Padé approximants vs Padé approximants. I. Numerical results
    arXiv:2306.07063, submitted on 12 Jun 2023, 26 p.
  5. M. A. Botchev, L. A. Knizhnerman, M. Schweitzer
    Solving large linear systems of second order differential equations by Krylov subspaces: residual and restarting
    Proceedings of the All-Russian conference "Scientific theory of the numerical algorithms construction and the solution of the mathematical physics problems", dedicated to the memory of K. I. Babenko, 24-26 August 2022, Pushchino, Moscow Region, Moscow 2022, p. 33-34.
  6. M.A. Botchev, L.A. Knizhnerman, M. Schweitzer
    Krylov subspace residual and restarting for certain second order differential equations
    arXiv:2206.06909, submitted on 14 Jun 2022, 26 p.
  7. V. Druskin, S. Güttel and L. Knizhnerman
    Model order reduction of layered waveguides via rational Krylov fitting
    BIT Numer. Math., 2022, v. 62, p. 1551-1572.
  8. Mike A. Botchev, Leonid Knizhnerman, and Eugene E. Tyrtyshnikov
    Residual and Restarting in Krylov Subspace Evaluation of the $\varphi$ Function
    SIAM J. Sci. Comput., 2021, v. 43, issue 6, p. A3733–A3759.
  9. L. A. Knizhnerman, A. L. Pleshkevich
    An algorithm of solution of an inverse dynamical acoustical problem for a vertically inhomogeneous medium and a pointwise source
    Proc. IV International geological and geophysical conference "GeoEvrasia-2021", v. I, p. 259-262. (In Russian)
  10. Sofia Davydycheva, Vladimir Druskin, Leonid Knizhnerman, and Michael Rabinovich
    Quality control of ultra-deep resistivity imaging using fast 3D electromagnetic modeling
    SEG Technical Program Expanded Abstracts 2020, p. 380-384.
  11. Mike A. Botchev, Leonid A. Knizhnerman, Eugene E. Tyrtyshnikov
    A residual concept for Krylov subspace evaluation of the φ matrix function
  12. Mikhail A. Botchev, Leonid A. Knizhnerman
    ART: adaptive residual-time restarting for Krylov subspace matrix exponential evaluations
    Journal of Computational and Applied Mathematics, 2020, v. 364, p. 2-14.
  13. L. A. Knizhnerman
    Numerical modelling of monochromatic acoustic waves generated by a point source in a depth-inhomogeneous semispace with use of an absorbing boundary condition
    Proc. of the International geological and geophysical conference GeoEurasia-2020, Moscow, February 3-6 2020, v. III, p. 85-88 (in Russian)
  14. V. L. Druskin, M. Yu. Zaslavsky, L. A. Knizhnerman
    Application of the Rational Arnoldi Method to approximate computation of matrix functions with a parameter
    Abstracts of the conference "Model problems of Computational Mathematics and Mathermatical Physics" dedicated to the 100th anniversary of academician's A.A.Samarskiy's birth Moscow, MSU, June 18-20 2019, p. 93-94 (in Russian)
  15. V. L. Druskin, M. Yu. Zaslavsky, L. A. Knizhnerman
    Optimized application of the Rational Arnoldi Method to approximate solution of two nonstationary electrical prospecting problems
    XVII International Conference "Supercomputing and mathematical modeling, Sarov, October 15-19, 2018, abstracts, p. 57-58 (in Russian).
  16. L. A. Knizhnerman
    Review of computational mathematical projects of the Mathematical Modelling Department of the Central Geophysical Expedition
    Materials of the XVth Internationa conference "Algebra, Number Theory and Discrete Geometry: modern problems and applications", dedicated to the 100th anniversary of birth of Dr. of Phys. and Math. Sci., professor of the Lomonosov MSU Nikolay Mikhailovich Korobov Tula, May 28-31 2018, p. 350-353. (in Russian)
  17. L. A. Knizhnerman, M. D. Khusid, T. F. Dyakonova
    Application of the consecutive lateral correction method to the solution of the axisymmetric inverse problem of electrical and induction logging in geological areas with diagonally-anisotropic beds
    Geofizika, 2017, special issue devoted to 50th anniversary of CGE, p. 118-125 (in Russian)
  18. V. Druskin, S. Güttel and L. Knizhnerman
    Compressing variable-coefficient exterior Helmholtz problems via RKFIT
    MIMS Eprint 2016.53.
  19. Kashik A. S., Knizhnerman L. A., Kosenkov O. M., Khusid M. D., Klimenko V. A., Salahov T. R., Shakurov D. R., Yulmuhametov C. R.
    Estimation of the efficiency of the high-resolution multi-electrode lateral logging tool and the software package for processing its measurements
    Neft'. Gaz. Novatsii, 2016, № 10, p. 64-71. (in Russian; there exists an English translation).
  20. A. S. Kashik, L. A. Knizhnerman, M. D. Khusid
    The design change of the casing with the purpose of optimization of development of deposits of hydrocarbons
    Burenie i neft', 2016, # 9, p. 56-60 (in Russian).
  21. V. Druskin, S. Güttel and L. Knizhnerman
    Near-optimal perfectly matched layers for indefinite Helmholtz problems
    SIAM Review, 2016, v. 58, No 1, p. 90-116.
  22. A. S. Kashik, L. A. Knizhnerman, O. M. Kosenkov, M. D. Khusid
    Development of a package of computational mathematical programs for handling measurements of a multi-electrode laterolog tool MnBK
    XXIth scientific and practical conference \"New technique and technologies for geophusical investigations of boreholes\", abstracts, p. 41-53. Ufa, NPF Geofizika, 2015
  23. M. D. Khusid, A. S. Kashik, L. A. Knizhnerman
    Current situation and future prospects of electrical logging in wells, cased with metal column
    Proceedings of the VIII-th Chinese-Russian symposium on Geophysics, China, Beijing, 2014, p. 45-54.
  24. P. Childs, V. Druskin, L. Knizhnerman
    Preconditioning the Helmholtz Equation using approximate Dirichlet-to-Neumann operators on optimal grids
    IMA Conference on Numerical Linear Algebra and Optimization, University of Birmingham, September 2014.
  25. Khusid M. D., Kashik A. S., Knizhnerman L. A.
    Optimizing the electrologging and electro-thermal effects in cased wells via the transformations of the column's construction
    Geofizika, 2014, No 4, p. 69-73 (in Russian).
  26. A. S. Kashik, L. A. Knizhnerman, M. D. Khusid
    Technology of enhanced oil recovery in deposits with hard to recover reserves via the electro-thermal stimulation of the near-wellbore area
    Proceedings of the 4-th International conference on topical issues of innovative oil and gas industry development ENERCON-2013, Moscow, 2013 (in Russian).
  27. Y. Lin, A. Abubakar, T. M. Habashy, G. Pan, M. Li, V. Druskin, L. Knizhnerman
    Schemes for improving efficiency of pixel-based inversion algorithms for electromagnetic logging-while-drilling measurements
    SEG Technical Program Expanded Abstracts 2012: 1-5.
  28. M. D. Khusid, A. S. Kashik, L. A. Knizhnerman, A. R. Klepatsky
    Modeling of high-viscosity oil and natural bitumen deposits development using electro-thermal stimulation with simultaneous control of the oil saturation beyond the column
    Geofizika, 2012, Special issue to the 45th anniversary of CGE, p. 117-122 (in Russian).
  29. S. Güttel and L. Knizhnerman
    A black-box rational Arnoldi variant for Cauchy-Stieltjes matrix functions
    BIT, 2013, v. 53, issue 3, p. 595-616.
  30. A. S. Kashik, L. A. Knizhnerman, A. R. Klepatsky, M. D. Khusid
    Modeling electro-thermal stimulation methods of the near-wellbore area during the development of high-viscosity oil deposit
    Exposition Oil Gas, 2012, p. 68-72 (in Russian).
  31. L. A. Knizhnerman and S. V. Shchedrina
    Use of a multiple precision arithmetic program of solving a direct axial symmetric problem to simulate some logging sonde
    Geofizika, 2012, a special issue to the 45th anniversary of CGE, p. 129-132. (In Russian).
  32. L. A. Knizhnerman
    A refined formula of the synthetic algorithm of sonde KR-1 for electrical logging through a steel casing
    Geofizika, 2012, a special issue to the 45th anniversary of CGE, p. 123-128. (In Russian).
  33. A. S. Kashik, L. A. Knizhnerman, M. D. Khusid
    Modeling electro-thermal stimulation methods during the development of high-viscosity oil and natural bitumen deposits
    XIX-th Gubkin’s reading "Innovative technologies forecasting, prospecting, exploration and exploitation of hydrocarbon accumulations and priority directions of the resource base development in Russian fuel and energy sector", RSUOG, 2011, p. 79-80 (in Russian).
  34. Yong‐Hua Chen, Dzevat Omeragic, Vladimir Druskin, Chih‐Hao Kuo, Tarek Habashy, Aria Abubakar, Leonid Knizhnerman
    2.5D FD modeling of EM directional propagation tools in high‐angle and horizontal wells
    SEG Technical Program Expanded Abstracts 2011: 422-426.
  35. S. Güttel and L. Knizhnerman
    Automated parameter selection for rational Arnoldi approximation of Markov functions
    PAMM Proc. Appl. Math. Mech., 2011, v. 11, issue 1, p. 15-18.
  36. M. Zaslavsky, V. Druskin and L. Knizhnerman
    Solution of 3D time-domain electromagnetic problems using optimal subspace projection
    Geophysics, 2011, v. 76, issue 6, p. F339–F351.
  37. V. Druskin, L. Knizhnerman and V. Simoncini
    Analysis of the rational Krylov subspace and ADI methods for solving the Lyapunov equation
    SIAM J. Numer. Anal., 2011, v. 49, No. 5, p. 1875-1898.
  38. M. Zaslavsky, V. Druskin, S. Davydycheva, L. Knizhnerman, A. Abubakar and T. Habashy
    Hybrid finite-difference integral equation solver for 3D frequency domain anisotropic electromagnetic problems
    Geophysics, 2011, v. 76, No. 2, p. F123-F137.
  39. L. Knizhnerman and V. Simoncini
    Convergence analysis of the Extended Krylov Subspace Method for the Lyapunov equation
    Numerische Mathematik, 2011, v. 118, No. 3, p. 567-586.
  40. L. Knizhnerman and V. Simoncini
    A new investigation of the extended Krylov subspace method for matrix function evaluations
    Numerical Linear Algebra with Applic., 2010, v. 17, No. 4, p. 615–638.
  41. S. I. Bilibin, A. S. Kashik, A. R. Klepatsky, L. A. Knizhnerman, M. D. Khusid
    The solution of the direct problems of electrical logging as the basis of the theory of methods’ development for viscous oil’s controlled extraction
    roceedings of the VI-th Chinese-Russian symposium on Geophysics, Part II, China, Qingdao, 2010, p. 72-87.
  42. V. Druskin, L. Knizhnerman and M. Zaslavsky
    Solution of large scale evolutionary problems using rational Krylov subspaces with optimized shifts
    SIAM J. Sci. Comp., 2009, v. 31, No. 5, p. 3760-3780.
  43. L. Knizhnerman
    Sensitivity of the Lanczos recurrence to Gaussian quadrature data: How malignant can small weights be?
    J. Comp. Appl. Math., 2010, v. 233, No. 5, p. 1238-1244.
  44. L. A. Knizhnerman
    Pade-Faber approximation of Markov functions on real-symmetric compact sets
    Math. Notes, 2009, v. 86, No. 1, p. 81-92.
  45. L. Knizhnerman, V. Druskin and M. Zaslavsky
    On optimal convergence rate of the Rational Krylov Subspace Reduction for electromagnetic problems in unbounded domains
    SIAM J. Numer. Anal., 2009, v. 47, № 2, pp. 953-971.
  46. A. Abubakar, T. M. Habashy, V. L. Druskin, L. Knizhnerman, and D. Alumbaugh
    2.5D forward and inverse modeling for interpreting low-frequency electromagnetic measurements
    Geophysics, 2008, v. 73, № 4, pp. F165–F177.
  47. L. A. Knizhnerman
    Gauss-Arnoldi quadrature for $ igllangle(zI-A)^{-1}varphi,,varphi igr angle$ and rational Pad'e-type approximation for Markov-type functions
    Math. Digest, 2008, v. 199, No. 2, pp. 27-48.
  48. Y. Zhang, A. Abubakar, T. Habashy, V. Druskin, L. Knizhnerman
    Parametric inversion algorithm for marine controlled‐source electromagnetic data
    SEG Technical Program Expanded Abstracts 2007: 569-573.
  49. V. L. Druskin, L. A. Knizhnerman
    Review of main investigations of the CGE's Mathematical Modelling Department for 1981-2006 years
    Geofizika, 2007, No. 4, pp. 61-65 (in Russian).
  50. D.L. Alumbaugh, A. Abubakar, V. Druskin, T. Habashy, A. Zerilli, L. Knizhnerman, G.M. Hoversten
    Fast 2D forward and inversion algorithms for interpreting marine CSEM data
    Offshore Technology Conference, 1-4 May 2006, Houston, Texas, USA.
  51. M. Zaslavsky, S. Davydycheva, V. Druskin, A. Abubakar, T. Habashy and L. Knizhnerman
    Finite-difference solution of the three-dimensional electromagnetic problem using divergence-free preconditioners
    2006 SEG Annual Meeting, October 1 - 6, 2006 , New Orleans, Louisiana, 4 p.
  52. A. Abubakar, T. M. Habashy, V. Druskin, L. Knizhnerman and S. Davydycheva
    A 3D parametric inversion algorithm for triaxial induction data
    Geophysics, 2006, v. 71, p. 1-9.
  53. A. Abubakar, T. Habashy, V. Druskin, D. Alumbaugh, A. Zerelli, L. Knizhnerman
    Two‐and‐half‐dimensional forward and inverse modeling for marine CSEM problems
    SEG Technical Program Expanded Abstracts 2006: 750-754.
  54. A. Abubakar, T. M. Habashy, V. Druskin and L. Knizhnerman
    An enhanced Gauss-Newton inversion algorithm using a dual optimal grid approach
    IEEE Transactions on Geoscience and remote sensing, 2006, v. 44, № 6, p. 1419-1427.
  55. L. Borcea, V. Druskin and L. Knizhnerman
    On the sensitivity of Lanczos recursions to the spectrum
    Linear Algebra Appl., 2005, v. 396, pp. 103-125.
  56. A. Abubakar, T. M. Habashy, V. L. Druskin, D. Alumbaugh, P. Zhang, M. Wilt, H. Denaclara, E. Nichols, L. Knizhnerman
    A fast and rigorous 2.5D inversion algorithm for cross‐well electromagnetic data
    SEG Technical Program Expanded Abstracts 2005: 534-537.
  57. L. Borcea, V. Druskin and L. Knizhnerman
    On the continuum limit of a discrete inverse spectral problem on optimal finite difference grids
    Comm. Pure Appl. Math., 2005, v. 58, № 9, pp. 1231-1279.
  58. A. S. Kashik, N. I. Rykhlinsky, L. A. Knizhnerman, R. I. Krivonosov, A. S. Stepanov
    On the electrical logging of boreholes, cased with steel tubes, by cable apparatus
    Karotazhnik, 2004, issues 3-4 (116-117), pp. 8-23 (in Russian).
  59. L. Knizhnerman
    Stability estimates on the Jacobi and unitary Hessenberg inverse eigenvalue problems
    SIAM J. Matrix Anal. Appl., 2004, v. 26, № 1, pp. 154-169.
  60. Aria Abubakar, Tarek M. Habashy, Vladimir Druskin, Sofia Davydycheva, Hanming Wang, Tom Barber, Leonid Knizhnerman
    A three‐dimensional parametric inversion of multi‐component multi‐spacing induction logging data
    SEG Technical Program Expanded Abstracts 2004: 616-619.
  61. S. Asvadurov, L. Knizhnerman and J. Pabon
    Finite-difference modeling of viscoelastic materials with quality factors of arbitrary magnitude
    Geophysics, 2004, v. 69, № 3, pp. 817-824.
  62. F. O. Alpak, C. Torres-Verdín, K. Sepehrnoori, Sheng Fang and Leonid Knizhnerman
    An extended Krylov subspace method to simulate single-phase fluid flow phenomena in axisymmetric and anisotropic porous media
    Journal of Petroleum Science and Engineering, 2003, v. 40, № 3-4, pp. 121-144.
  63. S. Asvadurov, V. Druskin, M. N. Guddati and L. Knizhnerman
    On optimal finite difference approximation of PML
    SIAM J. Numer. Anal., 2003, v. 41, № 1, pp. 287-305.
  64. L. Knizhnerman
    Adaptation of the Lanczos and Arnoldi methods to the spectrum, or why the two Krylov subspace methods are powerful
    Chebyshev Digest, 2002, v. 3, No. 2, pp. 141-164.
  65. S. Asvadurov, V. Druskin and L. Knizhnerman
    Application of the difference Gaussian rules to solution of hyperbolic problems. II. Global expansion
    J. Comput. Phys., 2002, v. 175, № 1, pp. 24-49.
  66. S. Asvadurov, L. Knizhnerman and J. Pabon
    Finite-difference modeling of viscoelastic materials with quality factors Q of arbitrary magnitude
    Schlumberger-Doll Research, TR OFSR/RN/2001/151/RTMI/C.
  67. C. Torres-Verdin, V. L. Druskin, Sheng Fang, L. A. Knizhnerman and A. Malinverno
    A dual-grid nonlinear inversion technique with applications to the interpretation of dc resistivity data
    Geophysics, 2000, v. 65, № 6, pp. 1733-1745.
  68. V. Druskin and L. Knizhnerman
    Gaussian spectral rules for second order finite-difference schemes
    Numer. Algorithms, 2000, v. 25, № 1-4, pp. 139-159.
  69. S. Asvadurov, V. Druskin, L. Knizhnerman
    Application of the difference Gaussian rules to solution of hyperbolic problems
    J. Comput. Phys., 2000, v. 158, pp. 116-135.
  70. D. Ingerman, V. Druskin and L. Knizhnerman
    Optimal finite difference grids and rational approximations of the square root. I. Elliptic problems
    Communic. on Pure and Appl. Math., 2000, v. 53, № 8, pp. 1039-1066.
  71. L. Knizhnerman
    On GMRES-equivalent bounded operators
    SIAM J. Matrix Anal. Appl., 2000, v. 22, № 1, pp. 195-212.
  72. V. Druskin and L. Knizhnerman
    Gaussian spectral rules for the three-point second differences: I. A two-point positive definite problem in a semi-infinite domain
    SIAM J. Numer. Anal., 1999, v. 37, № 2, pp. 403-422.
  73. L. Knizhnerman
    Error bounds for the Arnoldi method: a set of extreme eigenpairs
    Linear Algebra and Appl., 1999, v. 296, № 1-3, pp. 191-211.
  74. V. L. Druskin, L. A. Knizhnerman and Ping Lee
    New spectral Lanczos decomposition method for induction modeling in arbitrary 3-D geometry
    Geophysics, 1999, v. 64, № 3, pp. 701-706.
  75. B. Anderson, T. Barber, V. Druskin, Ping Lee, E. Dussun, L. Knizhnerman and S. Davydycheva
    The response of multiarray induction tools in highly dipping formations with invasion and in arbitrary 3D geometries
    The Log Analist, 1999, v. 40, № 5, pp. 327-344.
  76. M. van der Horst, V. Druskin, L. Knizhnerman
    40. Modeling Induction Logs in 3-D Geometries
    Three-Dimensional Electromagnetics (1999): pp. 611-622.
  77. A. Greenbaum, V. L. Druskin, and L. A. Knizhnerman
    On solving indefinite linear systems by means of the Lanczos method
    J. Comput. Math. and Mathem. Phys., 1999, v. 39, No. 3, pp. 371-377.
  78. V. Druskin, L. Knizhnerman and T. Tamarchenko
    Fast difference-differential method for geophysical electrodynamics
    In: K.K. Roy, S.K. Verma, and K. Mallick (ed.), Advances in Deep Electromagnetic Exploration, Narosa Publishing House, New Delhi, India and Springer Verlag, Heidelberg, Germany, 1998.
  79. V. Druskin and L. Knizhnerman
    Extended Krylov subspaces: approximation of the matrix square root and related functions
    SIAM J. Matrix Anal. Appl., 1998, v. 19, № 3, pp. 755-771.
  80. V. Druskin, A. Greenbaum, and L. Knizhnerman
    Using nonorthogonal Lanczos vectors in the computation of matrix functions
    SIAM J. Sci. Comp., 1998, v. 19, № 1, pp. 38-54.
  81. B. I. Anderson, V. Druskin, Ping Lee, M. G. Luling, E. Schoen, J. Tabanou, P. Wu, S. Davydycheva, and L. Knizhnerman
    Modeling 3-D effects on 2-MHz LWD resistivity logs
    In: Transactions of the SPWLA (Society of Professional Well Log Analysts) Thirty-Eighth Annual Logging Symposium, June 15-18, 1997: Houston, Tex., Society of Professional Well Log Analysts, Paper N, 14 p.
  82. V. Druskin, L. Knizhnerman, S. Kostek and T. Tamarchenko
    Krylov subspace reduction and its extensions for option pricing
    Comput. Finance, 1997, v. 1, № 1.
  83. L. Knizhnerman
    The simple Lanczos process: error estimates for the Gaussian quadrature formula and their applications
    J. Comput. Math. and Mathem. Phys., 1996, v. 36, No. 11, pp. 5-19. (In Russian; translated into English)
  84. L. Knizhnerman
    On adaptation of the Arnoldi method to the spectrum
    Schlumberger-Doll Research, Res. Note #EMG-001-96-03, February 12, 1996.
  85. V. Druskin and L. Knizhnerman
    Exponential split preconditioning of Krylov subspaces to compute functions of elliptic operators, illustrated by the 3-D diffusion and Maxwell equations
    Schlumberger-Doll Research, Rep. № EMG-001-95-23, November 29, 1995.
  86. V. Druskin and L. Knizhnerman
    Krylov subspace approximation of eigenpairs and matrix functions in exact and computer arithmetic
    Numer. Linear Algebra with Appl., 1995, v. 2, № 3, pp. 205-217.
  87. L. A. Knizhnerman
    The quality of approximations to a well separated eigenvalue and location of Ritz values in the simple Lanczos process
    J. Comput. Math. and Mathem. Phys., 1995, v. 35, No. 10, pp. 1459-1475. (In Russian; translated into English)
  88. M. van der Horst, V. Druskin, L. Knizhnerman
    Modelling the response of induction logging tools in 3D geometries with the Spectral Lanczos Decomposition Method
    Schlumberger-Doll Research, Res. Note #EMG-001-95-18, September 18, 1995.
  89. L. Knizhnerman
    On adaptation of the Lanczos method to the spectrum
    Schlumberger-Doll Research, Res. Note #EMG-001-95-12, May 12, 1995.
  90. L. Knizhnerman, V. Druskin, Quing-Huo Liu, and F.J. Kuchuk
    Spectral Lanczos decomposition method for solving single-phase fluid flow in porous media
    Numer. Methods for Partial Different. Equations, 1994, № 10, pp. 569-580.
  91. V. Druskin, L. Knizhnerman
    Spectral approach to solving three-dimensional Maxwell's diffusion equations in the time and frequency domains
    Radio Science, 1994, v. 29, № 4, pp. 937-953.
  92. V. Druskin and L. Knizhnerman
    On application of the Lanczos method to solution of some partial differential equations
    J. Comput. Appl. Math., 1994, v. 50, № 1-3, pp. 255-262.
  93. Vladimir Druskin, Leonid Knizhnerman
    An efficient new method for solving large‐scale electromagnetic problems in inhomogeneous conductive media in the time and frequency domains
    SEG Technical Program Expanded Abstracts 1993: 358-359.
  94. A. Hordt, V. Druskin, L. Knizhnerman, and K.-M. Strack
    Interpretation of 3-D effects in deep transient electromagnetic (LOTEM) soundings in the Münsterland area (Germany)
    Geophysics, 1992, v. 57, № 9, pp. 1127-1137.
  95. L. A. Knizhnerman
    Error estimates for the Arnoldi method: the case of a normal matrix
    J. Comput. Math. and Mathem. Phys., 1991, v. 31, No. 1, pp. 5-16. (In Russian; translated into English).
  96. V. Druskin and L. Knizhnerman
    Evaluations for Krylov subspace approximation to internal eigenvalues of large symmetric matrices and bounded self-adjoint operators with continuous spectrum
    Schlumberger-Doll Research, Res. Note, September 2, 1992.
  97. V. Druskin and L. Knizhnerman
    The Lanczos optimization of a splitting-up method to solve homogeneous evolutionary equations
    J. Comput. Appl. Math., 1992, v. 42, № 2, pp. 221-231.
  98. L. A. Knizhnerman
    Computation of functions of unsymmetric matrices by means of the Arnoldi method
    J. Comput. Math. and Mathem. Phys., 1991, v. 31, No. 1, pp. 5-16. (In Russian; translated into English)
  99. V. L. Druskin, L. A. Knizhnerman
    Error estimates for the simple Lanczos process when computing functions of symmetric matrices and eigenvalues
    J. Comput. Math. and Mathem. Phys., 1991, v. 31, No. 7, pp. 970-983. (In Russian; translated into English)
  100. V. L. Druskin, L. A. Knizhnerman
    Two polynomial methods for the computation of functions of symmetric matrices
    J. Comput. Math. and Mathem. Phys., 1989, v. 29, No. 12, pp. 1763-1775. (In Russian; translated into English)
  101. A. S. Kashik, L. A. Knizhnerman
    On stabilization of the statements of geophysical inverse problems
    Geology and Geophysics, 1989, No. 1, pp. 126-129. (In Russian; translated into English)
  102. L. A. Knizhnerman
    A numerical method of continuation of potential fields from a bounded region of the Earth surface
    Izv. AN USSR, ser. "Physics of Solid Earth", 1988, No. 12, pp. 23-30. (In Russian; translated into English)
  103. V. L. Druskin, L. A. Knizhnerman
    A spectral semi-discrete method for the numerical solution of three-dimensional non-stationary electrical prospecting problems
    Izv. AN USSR, ser. "Physics of Solid Earth", 1988, No. 8, pp. 63-74. (In Russian; translated into English)
  104. L. A. Knizhnerman
    On applications of the optimal coefficients method to the numerical solution of some problems of mathematical physics
    Saratov Univ., "Investigations on number theory", 1988, pp. 32-38. (In Russian)
  105. V. L. Druskin, L. A. Knizhnerman
    On an iterative algorithm for the solution of a two-dimensional inverse electrical logging problem
    Geology and Geophysics, 1987, No. 9, pp. 118-123. (In Russian; translated into English)
  106. L. A. Knizhnerman, V. Z. Sokolinsky
    On exponential sums and sums of the Legendre symbol with large and small absolute values
    Saratov Univ., "Investigations on number theory", 1987, pp. 76-89. (In Russian)
  107. V. L. Druskin, L. A. Knizhnerman
    A method for the solution of direct problems of electrical logging and electrical prospecting with direct current
    Izv. AN USSR, ser. "Physics of Solid Earth", 1987, No. 4, pp. 63-71. (In Russian; translated into English)
  108. V. L. Druskin, L. A. Knizhnerman
    The use of operator series in orthogonal polynomials when computing functions of self-adjoint operators and the justification of the Lanczos phenomenon
    Moscow, IZMIR AN USSR, dep. at VINITI 02.03.1987, No. 1535-B27, 47 p. (In Russian)
  109. V. L. Druskin, A. S. Kashik, L. A. Knizhnerman, O. M. Kosenkov
    The solution of an inverse electrical logging problem for axial symmetric inhomogeneous models
    "Mathem. methods of identification in geological problems", Moscow, Nauka, 1985, pp. 109-116. (In Russian)
  110. L. A. Knizhnerman
    The effectiveness of recognition as a way of choosing a regularization parameter when analytically continuing potential fields by decomposing into Chebyshev series
    Izv. AN USSR, ser. "Physics of Solid Earth", 1985, No. 5, pp. 87-90. (In Russian)
  111. L. A. Knizhnerman
    Extraction of poles of potential fields by means of decomposition into Fourier-Chebyshev series
    Izv. AN USSR, ser. "Physics of Solid Earth", 1984, No. 11, pp. 119-123. (In Russian; translated into English)
  112. L. A. Knizhnerman
    The numerical solution of Cauchy's problem for the Laplace equation by means of decomposition into Fourier-Chebyshev series
    Izv. AN USSR, ser. "Physics of Solid Earth", 1984, No. 10, pp. 76-81. (In Russian; translated into English)
  113. V. A. Milashin, L. A. Knizhnerman
    A first attempt of optimization of schemes of field measurements by means of a computer
    VNIIOENG, "Oil and Gas Geology, Geophysics and Drilling", 1984, issue 8, pp. 24-26. (In Russian)
  114. L. A. Knizhnerman
    An error estimate for a nonlinear variational regularization method of determining poles of potential fields
    Ed. Board of the J. "Izv. Vuzov", ser. "Geol. and Prosp.", dep. at VINITI 09.09.1983, No. 5173-83 Dep., 15 pp. (In Russian)
  115. L. A. Knizhnerman
    An adaptive variational regularization method of soving Cauchy's problem for a two-dimensional Laplace equation
    Ed. Board of the J. "Izv. Vuzov", ser. "Geol. and Prosp.", dep. at VINITI 09.09.1983, No. 5170-83 Dep., 8 pp. (In Russian)
  116. V. L. Druskin, L. A. Knizhnerman
    On determination of the first boundary in a two-dimensional inverse problem of electrical prospecting
    Nauka, "Math. methods of identification of models in Geology", 1983, pp. 126-134. (In Russian)
  117. L. A. Knizhnerman, V. A. Kronrod, V. Z. Sokolinsky, V. V. Shchennikov
    On the numerical solution of a three-dimensional nonlinear Poisson equation
    Syb. Energ. Inst., "Numerical methods of Analysis", 1980, pp. 89-93. (In Russian)
  118. L. A. Knizhnerman
    A number-theoretical method of solving Cauchy's problem for Poisson's equation
    MSPI, dep. at VINITI 21.04.1980, No. 1568-80 Dep., 22 pp. (In Russian)
  119. L. A. Knizhnerman
    A number-theoretical method of solving some problems for partial differential equations
    MSPI, dep. at VINITI 26.02.1980, No. 712-80 Dep., 24 pp. (In Russian)
  120. L. A. Knizhnerman, V. Z. Sokolinsky
    Some estimates for rational exponential sums and sums of the Legendre symbol
    Uspekhi Matem. Nauk, 1979, v. 34, No. 3, pp.199-200.
  121. L. A. Knizhnerman, V. Z. Sokolinsky
    On unimprovability of A. Weil's estimates for rational exponential sums and sums of the Legendre symbol
    MSPI, dep. at VINITI 29.05.1979, No. 2152-79 Dep., 15 pp. (In Russian)
  122. L. A. Knizhnerman, V. A. Kronrod, V. Z. Sokolinsky
    Numerical solution of a nonlinear Poisson equation
    Journal of engineering physics, 1979, v. 36, p. 709–711.
  123. L. A. Knizhnerman, V. A. Kronrod, V. Z. Sokolinsky
    A numerical method to solve Poisson's equation with an enhanced order of accuracy
    MSPI, "Comput. Math. and Progr.", 1978, issue 7, pp. 12-14. (In Russian)
  124. V. A. Kronrod, L. A. Knizhnerman, V. Z. Sokolinsky
    Some numerical experiments on solving Poisson's equation by means of a fast converging economical method
    MSPI, "Comput. Math. and Progr.", 1978, issue 6, pp. 130-135. (In Russian)

List of patents

  1. Paul N. Childs, Ivan Graham, James Douglas Shanks, Vladimir L. Druskin and Leonid Knizhnerman
    Wave equation processing
    Patent WO 2014057440 A1, Schlumberger Technology B.V., 2014.
  2. Vladimir Druskin, Ping Lee and Leonid Knizhnerman
    Method, apparatus, and article of manufacture for solving 3d Maxwell equations in inductive logging applications
    Patent WO 1998028637 A2, Schlumberger Technology B.V, 1998.

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